Regular sequences for triangulated categories
Commutative Algebra
2025-09-15 v1 Category Theory
Abstract
This paper systematically develops a notion of regular sequences in the context of -linear triangulated categories for a graded-commutative ring . The notion has equivalent characterizations involving Koszul objects and local cohomology. The main examples are in the context of the Hochschild cohomology ring or the group cohomology ring acting on derived or stable categories. As applications, lengths of regular sequences provide lower bounds for level and Rouquier dimension.
Cite
@article{arxiv.2509.09941,
title = {Regular sequences for triangulated categories},
author = {Antonia Kekkou and Janina C. Letz and Marc Stephan},
journal= {arXiv preprint arXiv:2509.09941},
year = {2025}
}
Comments
37 pages; comments are welcome